Group sequential design for comparative diagnostic accuracy studies

Abstract

In the field of diagnostic medicine, comparative clinical trials are necessary for assessing the utility of one diagnostic test over another. The area under the receiver operating characteristic (ROC) curve, commonly referred to as AUC, is a general measure of a test's inherent ability to distinguish between patients with and without a condition. Standardized AUC difference is the most frequently used statistic for comparing two diagnostic tests. In therapeutic comparative clinical trials with sequential patient entry, fixed sample design (FSD) is unjustified on ethical and economical grounds and group sequential design (GSD) is frequently used. In this paper, we argue that the same reasoning exists for the comparative clinical trials in diagnostic medicine and hence GSD should be utilized in this field for designing trials. Since computation of the stopping boundaries of GSD and data analysis after a group sequential test rely heavily on Brownian motion approximation, we derive the asymptotic distribution of the standardized AUC difference statistic and point out its resemblance to the Brownian motion. Boundary determination and sample size calculation are then illustrated through an example from a cancer clinical trial.

Design of telehealth trials – Introducing adaptive approaches

“…area under the ROC curve (AUROC). Methodology for this case is demonstrated in a paper by Mazumdar and Liu [34].…”

Optimal Sampling Ratios in Comparative Diagnostic Trials

“…The statistics for comparing markers might be parametric (Mazumdar and Liu, 2003), or non-parametric (DeLong et al , 1988; Wieand et al , 1989). Let θ be the parameter in the ROC comparison, and $\hat{\theta }$ be the estimator.…”

“…We present the variance expressions for these statistics in Sections 2.1.2 and 2.2. A similar variance structure for a conventional binormal ROC statistic of Mazumdar and Liu (2003) is presented in Appendix A.…”

“…Variance expressions for a parametric receiver operating characteristic statistic When measurements of markers have bivariate normal distributions, Mazumdar and Liu (2003) provided expressions for the variances, v x and v y . Suppose that ( X 1 , X 2 ) ~ N {( μ 1d , μ 2d ), Σ d } for i =1, .…”

“…. , n , where $${\Sigma }_d=true(\begin{array}{cc}center{\sigma }_{1d}^2& center\rho {\sigma }_{1d}{\sigma }_{2d}\\ center\rho {\sigma }_1{\sigma }_{2d}& center{\sigma }_{2d}^2\end{array}true)$$ and $${\Sigma }_{\stackrel{‒}{d}}=true(\begin{array}{cc}center{\sigma }_{1\stackrel{‒}{d}}^2& center\rho {\sigma }_{1\stackrel{‒}{d}}{\sigma }_{2\stackrel{‒}{d}}\\ center\rho {\sigma }_{1\stackrel{‒}{d}}{\sigma }_{2\stackrel{‒}{d}}& center{\sigma }_{2\stackrel{‒}{d}}^2\end{array}true).$$ The statistic considered in Mazumdar and Liu (2003) is the partial AUC estimator given by $${\hat{\theta }}_p^{bn}={\int }_{c_1}^{c_2}\Phi ({\alpha }_1-{\beta }_{1}x)\varphi \left(x\right)\mathrm{d}x-{\int }_{c_1}^{c_2}\Phi ({\alpha }_2-{\beta }_{2}x)\varphi \left(x\right)\mathrm{d}x,$$ where α 1 = ( μ 1d – μ 1 d̄ )/ σ 1 d , β 1 = σ 1 d̄ / σ 1 d and α 2 = ( μ 2 d – μ 2 d̄ )/ σ 2 d and β 2 = σ 2 d̄ / σ 2 d . Let $${\Gamma }_1(r,s;c_1,c_2)={\phantom{true\mid }\frac{1}{\surd (s^2+1)}\varphi \left\{\frac{r}{\surd (s^2+1)}\right\}\Phi \left(x\right)\mid }_{c_1^{\prime }}^{c_2^{\prime }}$$ and $${\Gamma }_2...$$…”